As set forth in FIG. 1, a microwave waveguide 10 is generally a system of four walls 30, 40, 50, defining a channel of rectangular cross section along which microwaves propagate. The broad walls 30 are generally perpendicular to the plane of the web 20 and contain a slot 60 through which the web 20 moves. The remaining two walls 40, 50 of the rectangular cross section are the narrow walls. Systems for microwave drying of webs have employed slotted waveguides with the slots along the centerlines of the waveguide broad walls. Typically, the web passes through a linear slot in the midplane of the waveguide, i.e., the centerline of the waveguide broad walls, and optionally travels through a series of serpentine waveguide elements. The prior microwave dryers resulted in non-uniform drying of the web across its width because of the decay in the microwave energy across the waveguide causing the microwave energy to be absorbed differently across the web width.
U.S. Pat. No. 5,958,275 proposed to improve drying uniformity, primarily in non-paper substrates, by linearly varying the position of the web along the guide, i.e., the slot height changes along the waveguide. See FIG. 2. The '275 patent relates to a method for compensating for attenuation when drying planar materials in a side-fed, rectangular waveguide driven in the TE10 mode. The web passes through a slotted guide 60 along the short direction, so that the guide electric field is in the plane of the web.
FIGS. 1 and 2 depict a slotted waveguide 10 having a linear opening in the broad wall 30 according to the prior art. The paper web 20 passes through the slotted waveguide 10.
Ignoring the effects of the web and the slot, the electric field amplitude has a half-wave sine variation between the long ends of the guide. The field is null at the guide top wall 40 and the bottom wall 50, and has a peak at the guide center. The field is independent of position in the guide short direction. As the electromagnetic wave propagates down the guide in the z direction, it attenuates due to dissipation in the web. Thus, normally, the intensity of heat generation decreases along the guide. The '275 patent proposes to fix this by linearly varying the position of the web along the guide. The slot height changes along the guide. See FIG. 2. In the beginning, before the wave is much attenuated, the web is near the lower guide wall 50, where the field amplitude is relatively small. As the wave propagates and attenuates, the height of slot changes to move the web toward the center of the guide. Here, the field is relatively stronger which can allow the maintenance of a more uniform intensity of heat dissipation.
The '275 patent discusses the use of a diagonal slot to roughly compensate for attenuation by moving the web to higher electric field regions away from the source. However, when significant compensation is necessary, as can be the case in the production of paper, a straight diagonal slot is insufficient.
It has not been recognized that a slot height that varies in a non-linear manner with cross-machine position (relative to the narrow wall) can be designed to achieve better heating uniformity. In embodiments according to the present invention, this configuration can allow for complete compensation for the reduction in peak electric field strength due to absorption in the web as the waves propagate across the width of the web.